ENGLISH

Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces, 1st Edition

By Walter Benz

Book information

Publisher
Birkhäuser Basel
Year
2005
ISBN
9783764373719, 9783764374327, 3764373717
LCC
QA431 .B39 2005
Open Library ID
OL22718894M
Language
english
Format
PDF
Filesize
2 MB (1754681 bytes)
Edition
1
Pages
251\251
Orientation
yes
Scanned
no
Time added
2011-06-04 13:46:07

Description

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of M?bius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

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